procedure rolling moment report.pdf
TRANSCRIPT
-
Rolling moment due to rate of role Introduction When an aircraft to roll, a resistance to the rolling is generated by the wing, the dimensionless
rolling moment is an important parameter of the lateral stability of an aircraft and it is equal to
the roll rate of the wing. This rolling moment is important since it contribute to the aircraft stability.
The can be estimated theoretically (simple strip theory, modified strip theory and lifting line
theory) for elliptical and tapered wings.
Derivation for theoretical estimate for of straight tapered wing
Simple strip theory
The rolling moment is defined by
=1
2
2 2 2
=
1
2
2 =1
2 (2)
2
=
(2)2/ 2
Modified strip theory
It can be adjusted to:
=
14.30{1+
}
Lifting line theory
=
14.30{1+2
}
Apparatus
A straight tapered wing of moderate AR mounted on a freely rotating shaft in the working section of
open wind tunnel.
A pan to carry the weight attached to a bobbin by a rope.
A three kilograms
Procedure 1 The atmospheric pressure and the temperature were recorded.
2 The span of the tapered wing was measured.
-
3 The distance travelled by the weight pan after ten revolutions was measured in order to estimate
the effective radius of the bobbin, in which the chord is wounded
4 The chord rewind by turning the lever handle clockwise
5 The weight pan was released from the rest and the wind tunnel reference pressure indicated
10.5mmH2O for the first set of the experience.
6 An increasing mass by 0.5 Kg increment up to 3 Kg clockwise and anticlockwise.
7 The rolling moment were recorded for each mass increment.
8 the steps 5, 6 and 7 were repeated for higher values of tunnel reference pressure 12.6 and
15mmH2O.
Results
Atmospheric pressure, P= 762.4 mmHg.
Atmospheric temperature, T = 21C.
Span=0.502m
Tip chord=0.06m
Root chord=0.125m
Wing surface=0.04642
Bobbin radius=0.0102m
For 10.5mmH2O
Mass (kg) Time period Clockwise(s)
Time period Anticlockwise(s)
Impulse, L/U (Ns)
Roll rate , P (rad/s) clockwise
Roll rate, P (rad/s) anticlockwise
Freestream Velocity
V(
)
0 31.01 42.38 0 2.026180363
-1.482582659
14.54488273 0.5 15.36 17.86 0.0037669
23 4.0906154
34 -
3.518020889
1 9.02 10.31 0.007533846
6.965837369
-6.09426315
1.5 7.03 7.21 0.011300769
8.93767469
-8.714542728
2 5.38 5.39 0.015067692
11.6787831
-11.6571156
2.5 3.83 3.9 0.018834615
16.40518357
- 16.11073156
-
For 12.5mmH2OO
Mass (kg) Time period Clockwise
(s)
Time period Anticlockwise
(s)
Impulse,
L/U (Ns)
Roll rate , P (rad/s) clockwise
Roll rate, P (rad/s) anticlockwise
Freestream Velocity
V(
)
13.27760061
0 31.28 44.29 0 2.0086909
55
-
1.4186464
91
0.5 15.92 18.19 0.0034387
15
3.9467244
39
-
3.4541975
3
1 10.2 11.32 0.0068774
29
6.1599855
95
-
5.5505170
56
1.5 7.19 8.18 0.0103161
44
8.7387834
59
-
7.6811556
32
2 6.13 6.01 0.0137548
58
10.249894
47
-
10.454551
26
2.5 4.95 5.19 0.0171935
73
12.693303
65
-
12.106330
07
Table 2
For 15mmH2O
Mass (kg) Time period Clockwise(s)
Time period Anticlockwise(s)
Impulse,
L/U (Ns)
Roll rate , P (rad/s) clockwise
- Roll rate, P (rad/s)
anticlockwise
Freestream Velocity
V(
)
15.86976812
0 32.27 46.38 0 1.94706703 -
1.354718695
0.5 16.11 18.97 0.003151634 3.900177099 -
3.312169376
1 11.08 12.36 0.006303268 5.670744862 -
5.083483258
1.5 8.09 8.97 0.009454902 7.766607302 -
7.004665894
2 6.2 7.17 0.012606536 10.13416985 -
8.763159424
2.5 5.16 5.93 0.01575817 12.17671571 -
10.59559074
Table 3
-
Gradient of the linear portion L vs p
graph
Experimental
Speed Clockwise Anticlockwise
clockwise
anticlockwise mmH2O
10 0.0015 -0.0014 0.00704006 0.213066356 -
0.198861932
12 0.0014 -0.0016 0.00704006 0.198861932 -0.22727078
14 0.0014 -0.0017 0.00704006 0.198861932 -
0.241475203
=
0.3787846
Table 4
Figure 1 shows the rolling moment vs roll rate clockwise and anticklocwise
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-20 -15 -10 -5 0 5 10 15 20
L/ N
m
ROLL RATE (P)/RAD S-1
Applied rolling moment Vs roll rate 10.5mmH2O
clockwise
anticlockwise
-
Figure 2 shows the rolling moment vs roll rate clockwise and anticklocwise
Figure 3shows the rolling moment vs roll rate clockwise and anticklocwise
Calculation of chordial Reynolds number Reynolds number is given by the following equation
=
=2
=0.046435
0.502=0.0925
For 10.5mmH2O correspend for 13.27m/s
=1.20313.27760.0925
1.813105 =81490.9
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-15 -10 -5 0 5 10
L/ N
m
ROLL RATE (P)/RAD S-1
Applied rolling moment Vs roll rate 12.5mmH2O
clockwise
anticlockwise
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-15 -10 -5 0 5 10 15
L/ N
m
ROLL RATE (P)/RAD S-1
Applied rolling moment Vs roll rate 15mmH2O
clockwise
anticlockwise
-
For 12.5mmH2O corrspend for 14.54488273
=1.20314.544880.0925
1.813105 =89272.9
For 15mmH2O corrspend for 15.869768
=1.20315.8697680.0925
1.813105 =97404.332
Calculation angle of attack
= tan1
Where is the rate of roll at stalling and can be approximated from the graph of Applied rolling
moment against roll rate at the point where the curve diverges from the linear portion and y is the
distance from OX axis.
For 13.277m/s p=0.213
= 17.22 For clockwise and = 17.44 for anticlockwise
For 14.544m/s p=0.19886
= 12.355 For clockwise and = 11.97 for anticlockwise.
For 15.869m/s p=0.19886
= 10.9 for clockwise and = 9.6 for anticlockwise.
Calculating theoretical values of Lp
Strip theory
=(
L
p)p0
1
2(2)2
= 16
The strip theory is applied for two values of, 5.7 1 and 21
For 5.7 1
= 0.356
For 21
= 0.3927
Modified strip theory
=
16{1+
} And applied for two values, 5.7 1 and 21
=(2)2
=
0.252
0.0464=4.74
For 5.7 1 Lp=-0.267
21 = 0.287
-
Lifting line theory
=
16{1+2
} And applied for two values, 5.7 1 and 21
5.7 1
= 0.201
= 0.215
For straight tapered wing
Strip theory
For 5.7 1 = 0.3986
21 = 0.439
Modified strip theory
For 5.7 1 = 0.299
21 = 0.3215
Lifting line theory
For 5.7 1 = 0.2394
21 = 0.25354 .
Error calculations
The percentage error can be calculated as follow:
100
The average experimental values of = 0.3787846
The percentage error for the elliptical wing and the experimental results
1 Strip theory Modified strip theory Lifting line theory
5.7 20.6% 24.16% 27.702%
2 19.4% 23.18% 26.71%
Table 5
The percentage error for the tapered wings and the experimental results
1 Strip theory Modified strip theory Lifting line theory
5.7 19.50% 22.66% 25.82%
2 18.62% 21.78% 24.93%
Table 6
Discussion:
The figure 1,2 and 3 show that when the air speed increase the rolling moment increase and this
could be obvious because the wing has larger rolling moment to resist and also it was notice that as
the air speed increased, the linear portion of the curve became larger, which means that the angle of
-
attack, at which the wing stall, increased. The stall, which occurs at lower angle of attack for lower
speed suggest that the drag affect the roll rate.
The figure 1,2and 3 show also that the linear part of the clockwise part is larger than the one for
anticlockwise, which suggest less effect for the rolling moment at the anticlockwise to resist the roll.
The experimental values of and the theoretical calculated one are largely different.
Comparing the results shows that the theoretical elliptical results are closer to the experimental
than the tapered wing one
Errors
There are many source of error in the experimental.
The human error, which occurs from recording the time. The pan weight may release before the
timing starts either the opposite is true. Recording the time more than one and allows more than
ten revolutions if there is a space can reduce this error.
The pressure difference seems to be not fixed because the fluctuations again running more than one
time the experiment can reduce the error.
Conclusion
In this report the theoretical values for the rolling moment were calculated, for the elliptical and
tapered wings and the values from the experiment were calculated.
There were significant difference between the theoretical and experimental results. Nevertheless,
the experiment shows the effect of increasing speed on the angle of attack and the rolling moment,
which is very realistic.
The experiment can be more successful if considering to reduce the error to minimum.
References R.Vepa, lecture notes, Queen Mary university of London, 2014.
Lab hand-out note, Queen Mary university of London,2014
-
Appendix
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-20 -15 -10 -5 0 5 10 15 20
L/ N
m
ROLL RATE (P)/RAD S-1
Applied rolling moment Vs roll rate 15mmH2O
10.5clockwise
10.5anticclowise
12.5clockwise
12.5anticklockwise
15clockwise
15anti
y = 0.0014x - 0.0021
y = -0.0016x - 0.0022
0
0.002
0.004
0.006
0.008
0.01
0.012
-10 -5 0 5 10
L/ N
M
ROLL RATE (P)/RAD S-1
+ 12.6mmH2O
- 12.6mmH2O
Linear (+ 12.6mmH2O)
Linear (- 12.6mmH2O)
-
x x bar x-xbar (x-xbar)squared
(x-xbar)squared/6 SIGMA
0.21306636 0.21306636 2.22045E-16 4.93038E-32 0.000269021 0.01640186
0.19886193 -0.01420442 0.000201766
0.19886193 -0.01420442 0.000201766
0.19886193 -0.01420442 0.000201766
0.22727078 0.014204424 0.000201766
0.2414752 0.028408847 0.000807063
y = 0.0014x - 0.0018
y = -0.0017x - 0.0025
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
-20 -10 0 10 20
L/ N
m
ROLL RATE (P)/RAD S-1
+ 15mmH2O
- 15mmH2O
Linear (+ 15mmH2O)
Linear (- 15mmH2O)
y = 0.0015x - 0.0026
y = -0.0014x - 0.001
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
-20 -10 0 10 20
L/ N
m
ROLL RATE (P)/RAD S-1
+ 10.5mmH2O
- 10.5mmH2O
Linear (+ 10.5mmH2O)
Linear (- 10.5mmH2O)